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Exponents - Power Law - Prime Base with Variable Power to Composite Base with Unknown Power (Level 1)

This math topic focuses on solving for missing exponents using the power law, a fundamental concept in exponents. Each problem presents equations where the base and/or exponent are either a prime or a composite number, and the task is to find the unknown exponent that makes the equation true. Problems are written to strengthen understanding of how to manipulate and simplify expressions involving powers and to develop skills in algebraic thinking related to exponential relationships. The problems incrementally build on the concept of exponents by exploring different bases and their corresponding powers.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Power Law - Prime Base with Variable Power to Composite Base with Unknown Power

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Solve for the missing exponent (?) in reduced form

2n=4?2^{n} = 4^{?}

Exponents - Power Law - Prime Base with Variable Power to Composite Base with Unknown Power Worksheet

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Math worksheet on 'Exponents - Power Law - Prime Base with Variable Power to Composite Base with Unknown Power (Level 1)'. Part of a broader unit on 'Exponents - Multiplication and Division - Advanced' Learn online: app.mobius.academy/math/units/exponents_multiplication_and_division_advanced/
1
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 2 to the power of n = 4 to the power of ?
a A LaTex expression showing ?=4 over n
b A LaTex expression showing ?=4n over 1
c A LaTex expression showing ?=2n
d A LaTex expression showing ?=2n over 2
e A LaTex expression showing ?=1 over 2n
f A LaTex expression showing ?=n over 2
2
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = 64 to the power of ?
a A LaTex expression showing ?=n over 3
b A LaTex expression showing ?=4n over 3
c A LaTex expression showing ?=5n
d A LaTex expression showing ?=4 over 3n
e A LaTex expression showing ?=1 over 2n
f A LaTex expression showing ?=n over 2
3
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 2 to the power of n = 8 to the power of ?
a A LaTex expression showing ?=12n
b A LaTex expression showing ?=2n over 3
c A LaTex expression showing ?=3n
d A LaTex expression showing ?=n over 3
e A LaTex expression showing ?=3n over 3
f A LaTex expression showing ?=9 over n
4
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 4 to the power of n = 16 to the power of ?
a A LaTex expression showing ?=1 over 2n
b A LaTex expression showing ?=n
c A LaTex expression showing ?=2n over 2
d A LaTex expression showing ?=4n over 1
e A LaTex expression showing ?=n over 2
f A LaTex expression showing ?=4 over 2n
5
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 6 to the power of n = 36 to the power of ?
a A LaTex expression showing ?=n over 3
b A LaTex expression showing ?=1 over 3n
c A LaTex expression showing ?=6 over n
d A LaTex expression showing ?=n over 2
e A LaTex expression showing ?=3n over 2
f A LaTex expression showing ?=n
6
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 5 to the power of n = 25 to the power of ?
a A LaTex expression showing ?=1 over 2n
b A LaTex expression showing ?=6n
c A LaTex expression showing ?=4n over 1
d A LaTex expression showing ?=4n
e A LaTex expression showing ?=4 over n
f A LaTex expression showing ?=n over 2
7
Solve for the missing exponent (?) in reduced form
A LaTex expression showing 3 to the power of n = 9 to the power of ?
a A LaTex expression showing ?=1 over 2n
b A LaTex expression showing ?=n over 2
c A LaTex expression showing ?=n
d A LaTex expression showing ?=3n over 2
e A LaTex expression showing ?=4n over 1
f A LaTex expression showing ?=4n